In a manner that is characteristic of or relates to calligraphy; with artistic, beautiful handwriting or lettering.
From calligraphic + the adverbial suffix '-ly', converting the adjective into an adverb describing how something is done.
Adding '-ly' to an artistic term like 'calligraphic' creates an interesting paradox—you can't really do something 'calligraphically' in speech, only in visual presentation, making this a word that's more useful in writing about writing.
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